Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution
Abstract
We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r^-(d+sigma). The long time dynamics of correlations and responses are studied in the different dynamical regimes and the validity of fluctuation-dissipation relations (or its violation) are shown. In particular, we show that the fluctuation-dissipation ratio X(t+t_w,t_w) is assymptotically a function only of the waiting time t_w in the aging regime and that X -> 0 as t_w -> oo . The results are valid in any finite dimension d and for 0 < sigma < 2, where short range behaviour is recovered. We also solve the T=0 Cahn-Hilliard dynamics of this model (conserved order parameter). An analysis of the multiscaling behaviour of the autocorrelation function is presented.
Cite
@article{arxiv.cond-mat/0010319,
title = {Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution},
author = {Sergio A. Cannas and Daniel A. Stariolo and Francisco A. Tamarit},
journal= {arXiv preprint arXiv:cond-mat/0010319},
year = {2009}
}
Comments
10 pages, no figures